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2022/23 Taught Postgraduate Module Catalogue

PHIL5660M Philosophy of Logic and Mathematics

30 creditsClass Size: 15

Module manager: Dr Jack Woods

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

Pre-requisite qualifications

An undergraduate module in formal logic or in metaphysics

This module is mutually exclusive with

MATH5021MPhilosophy of Logic and Mathematics
PHIL3123Philosophy of Logic & Maths

This module is not approved as an Elective

Module summary

The module examines philosophical issues concerning the philosophy of logic and mathematics including issues regarding paradoxes, vagueness, the nature of logics and logical constants, as well as the metaphysics of mathematical objects and theories of mathematics.


This module will enable students to understand and discuss critically, in detail, the philosophical issues concerning the nature and application of logic or mathematics; read, interpret and criticise historical and contemporary research on the subject. 

Learning outcomes
On successful completion of this module, students should be able to: 

Demonstrate advanced knowledge and understanding of issues in philosophy of logic and mathematics

Demonstrate the ability to critically engage with and evaluate complex and varied material in philosophy of logic and mathematics

Develop a critical and nuanced argument in essay form engaging with relevant material using their own independent critical skills and drawing on material from a range of relevant sources. 

Conduct independent research and make appropriate use of supervision structures. 


Students will study a selection from the following/relevantly similar topics:
- Philosophy of Mathematics Logicism (Frege, Russell, etc) Intuitionism (Kant and Kantians, Brouwer)
- Formalism (Hilbert): The metaphysics of mathematical objects: realism and nominalism. The epistemology of mathematics. The (unreasonable?) effectiveness of mathematics in the sciences. 
- Philosophy of Logic What is logic? 
- Logical constants; the scope of logic; higher order logic. 
- Logical concepts: philosophical analysis of one or more of: the conditional, quantifiers, negation, definite descriptions etc. 
- Alternative logics: free logic; many-valued and fuzzy logics; intuitionistic logic; relevance logics. 
- Modern theories of truth from Russell to the present: correspondence, redundancy, Tarski, minimalism, truthmaker theory. 
- Theories of vagueness: fuzzy logic, supervaluation, epistemic theories. Intensional logics, their uses and justifications. 
- Paradoxes: types and avoidance strategies. 
- Expanding logic: Generalised Quantifiers; Indexicals; Tense; Logic Diagrams. 
- Approached to logic: formalist; semantic; logic in use. 
- Logic and ontology. 
- Logic, cognition and natural language; non-monotonic logics.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Private study hours278.00
Total Contact hours22.00
Total hours (100hr per 10 credits)300.00

Private study

Weekly reading and preparation for seminars and tutorials: 9 x 10 = 90 hours

Research and preparation for essay: 100 hours

Essay writing (including drafts and revisions): 88 hours

Opportunities for Formative Feedback

Formative feedback will be given in: (i) seminars; (ii) a one-to-one supervision meeting where the module leader will comment and provide guidance and feedback on student essay plans of length 1000 words; and (iii) in office hours offered by the module leader and tutorial leader (if these are different).

Student progress will be monitored through submission of a 5,000 word essay submitted in Semester 2, Week 13, on which feedback will be provided.

Methods of assessment

Assessment typeNotes% of formal assessment
Essay5000 words100.00
Total percentage (Assessment Coursework)100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 29/04/2022 15:26:27


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